How do you solve 3x^2 + 10x - 2 = 0  by completing the square?

Oct 7, 2017

$x = \frac{\sqrt{31}}{9} - \frac{5}{3}$
$x = - \frac{\sqrt{31}}{9} - \frac{5}{3}$

Explanation:

Given -

$3 {x}^{2} + 10 x - 2 = 0$

Take the constant term to right-hand side

$3 {x}^{2} + 10 x = 2$

Divide both sides by 3

$\frac{3 {x}^{2}}{3} + \frac{10 x}{3} = \frac{2}{3}$

${x}^{2} + \frac{10}{3} x = \frac{2}{3}$

Divide the coefficient of $x$ by2; square it and add it to both sides

${x}^{2} + \frac{10}{3} x + \frac{100}{36} = \frac{2}{3} + \frac{100}{36} = \frac{24 + 100}{36} = \frac{124}{36} = \frac{31}{9}$
${\left(x + \frac{10}{6}\right)}^{2} = \frac{31}{9}$

$x + \frac{5}{3} = \pm \sqrt{\frac{31}{9}} = \pm \frac{\sqrt{31}}{3}$

$x = \frac{\sqrt{31}}{9} - \frac{5}{3}$
$x = - \frac{\sqrt{31}}{9} - \frac{5}{3}$